Method and apparatus for true random number generator based on nuclear radiation

ABSTRACT

A true random number generator (TRNG) is disclosed that includes an enclosure. The enclosure encloses a radioactive source defining a radioactive source surface and a cavity separating the radioactive source from an array of cells that define an array surface with an edge. Each cell in the array comprises a detector constructed to detect electrons within the cavity from the decay of the radioactive source and constructed to produce a signal for the detected energy. A projection of the radioactive source surface onto the array surface extends beyond the edge and encompasses the array surface.

1.0 PRIORITY APPLICATIONS AND REFERENCES

This application claims priority to U.S. Provisional Application Ser.No. 63/224,811 titled “Method and Apparatus for Highly Effective BetaDecay Based On-Chip True Random Number Generator”, filed on Jul. 22,2021; to U.S. Provisional Application Ser. 63/234,820 titled “Method AndApparatus For Highly Effective Beta Decay Based On-Chip True RandomNumber Generator”, filed on Aug. 19, 2021; to U.S. ProvisionalApplication Ser. 63/235,031 titled “Method And Apparatus For HighlyEffective Beta Decay Based On-Chip True Random Number Generator”, filedon Aug. 19, 2021; and to U.S. Provisional Application Ser. 63/270,912titled “Method And Apparatus For True Random Number Generator Based OnNuclear Radiation” filed on Oct. 22, 2021, all of which are incorporatedherein by reference in their entireties.

This application is also related to U.S. application Ser. No. 17/409,971filed on Aug. 24, 2021 and titled “Method And Apparatus For HighlyEffective On-Chip True Random Number Generator Utilizing Beta Decay”; toU.S. Provisional Application Ser. 62/984,528 filed on Mar. 3, 2020 andtitled “Method And Apparatus For Tritium-Based True Random NumberGenerator”; to U.S. Provisional Application Ser. 63/062,672 filed onAug. 7, 2020 and titled “Method And Apparatus For Beta Decay Based TrueRandom Generator”; to U.S. Provisional Application Ser. 62/655,172 filedon Apr. 9, 2018 and titled “Apparatus, Systems, And Methods ComprisingTritium Random Number Generator”; to U.S. Provisional Application Ser.62/803,476 filed on Feb. 9, 2019 and titled “Apparatus, Systems, AndMethods Comprising Tritium Random Number Generator”, now U.S. Pat. No.10,430,161; to U.S. application Ser. No. 16/273,365 filed on Feb. 12,2019 and titled “Apparatus, Systems, And Methods Comprising TritiumRandom Number Generator”; to U.S. application Ser. No. 16/990,087 filedon Aug. 11, 2020 and titled “Apparatus, Systems, And Methods For BetaDecay Based True Random Number Generator”, now U.S. Pat. No. 10,901,695;to U.S. application Ser. No. 17/126,265 filed on Dec. 18, 2020 andtitled “Method and Apparatus for Tritium-based True Random NumberGenerator”, now U.S. Pat. No. 11,048,478; to U.S. application Ser. No.17/062,307 filed on Oct. 2, 2020 and titled “Apparatus, Systems, AndMethods For Beta Decay Based True Random Number Generator”, now U.S.Pat. No. 11,036,473; to PCT Application SN PCT/US19/17748 titled“Apparatus, Systems, And Methods Comprising Tritium Random NumberGenerator” and filed on Feb. 13, 2019; to PCT Application SNPCT/US20/65962 titled “Apparatus, Systems, And Methods For Beta DecayBased True Random Number Generator” and filed on Dec. 18, 2020; and toPCT Application SNPCT/US20/65976 titled “Apparatus, Systems, And MethodsFor Beta Decay Based True Random Number Generator” and filed on Dec. 18,2020. Each of the patent applications, issued patents, and otherreferences discussed and/or cited herein, are incorporated by referenceas if fully set forth herein.

Referenced herein and also incorporated are the following: (1) M.-M. Béet al. 2008 Bureau International des Poids et Mesures, Sevres (France)BIPM-5 vol. 1-7 Table of Radionuclides; (2) Belghachi A. et al. 2020Acta Physica Polonica A vol. 137, no. 3, pp. 324 -331, A model of Ni-63source for betavoltaic application; and (3) Knechtel J. et al. 2017 PSJTransactions on System LSI Design Methodology vol. 10 pp. 45-62Large-Scale 3D Chips: Challenges and Solutions for Design Automation,Testing, and Trustworthy Integration.

2.0 TECHNICAL FIELD

The present disclosure relates generally to true random numbergenerators, specifically random number generator technologies utilizingthe spontaneous nickel isotope decay, as well as apparatus, systems, andmethods regarding the same.

3.0 BACKGROUND

As opposed to pseudo-random number generators based on numericalalgorithms, there are true random number generator (TRNG) devices thatdepend on natural random processes: multiple bipolar switches, thermalnoise, light scattering by dichroic mirrors, chaotic systems, and decayof radioactive nuclei. Some of these TRNGs are listed in the provisionalapplications to which the present application claims priority, and thosereferences are incorporated herein by reference as if fully set forthherein.

The decay of radioactive nuclei types is considered to be the mostindependent from environmental influences like temperature, pressure, oracceleration. However, typical nuclear-based TRNGs require large-sizeddetectors to enable the registration of particles emitted as a result ofradioactive decays. Also, many nuclei used in such devices are highlyradioactive and poisonous, hence dangerous to humans if a device isbroken.

Therefore, a safe and small TRNG that will not expose the user todangerous levels of radiation would be advantageous. Such a TRNG canthen be used in compact personal devices.

4.0 SUMMARY

A true random number generator (TRNG) is disclosed that includes anenclosure. The enclosure enfolds a radioactive source defining aradioactive source surface and a cavity separating the radioactivesource from an array of cells that define an array surface with an edge.Each cell in the array comprises a detector constructed to detectelectrons within the cavity from the decay of the radioactive source andconstructed to produce a signal for the detected energy. A projection ofthe radioactive source surface onto the array surface extends beyond theedge and encompasses the array surface.

The radioactive source may be nickel. The TRNG array surface may have acenter point, and the size of the detector in each cell is based on thedistance of the detector from the center point.

The TRNG may also include a memory connected to each detector in thearray of cells, wherein the memory stores the produced signals from thedetector. A TRNG processor may produce a true random number based on thecontents of the memory.

Additional aspects, alternatives, and variations, as would be apparentto persons of skill in the art, are also disclosed herein and arespecifically contemplated as included as part of the invention. Theinvention is set forth only in the claims as allowed by the patentoffice in this or related applications, and the following summarydescriptions of certain examples are not in any way to limit, define orotherwise establish the scope of legal protection.

5.0 BRIEF DESCRIPTION OF DRAWINGS

The invention can be better understood with reference to the followingfigures. The components within the figures are not necessarily to scale,emphasis instead being placed on clearly illustrating example aspects ofthe invention. In the figures, like reference numerals designatecorresponding parts throughout the different views and/or embodiments.Furthermore, various features of different disclosed embodiments can becombined to form additional embodiments, which are part of thisdisclosure. It will be understood that certain components and detailsmay not appear in the figures to assist in more clearly describing theinvention.

FIG. 1 illustrates a circuit for registering electron hits of thedetector.

FIG. 2A is a top view of a detector chip with a cell array matrix withthe cover and radioactive source made semi-transparent so that the arrayof detectors can be seen.

FIG. 2B is a cross-sectional view of a portion of a single detector chipwithin a cell array matrix with a cell array of FIG. 2A illustrating acircuit for registering electron hits of the detector using throughsilicon vias.

FIG. 3 illustrates a cross-section of a TRNG with a radioactive sourceand a matrix of detectors.

FIG. 4 illustrates the three regions from which a detector will detectelectrons from the decay of the radioactive source.

FIG. 5 is a graph of the electron flux v. distance from the edge of theTRNG chip for the TRNG of FIG. 3.

FIG. 6 illustrates a cross-section of a TRNG with a radioactive sourceand a matrix of detectors. Unlike FIG. 3, the source has a projectedsurface that is larger than the surface of the matrix of detectors.

FIG. 7 is a top view of the TRNG of FIG. 6, illustrating the cell arraymatrix surface circumscribed by the radioactive source (with extension)surface.

FIG. 8 is a graph of the electron flux v. distance from the edge of theTRNG chip for the TRNG of FIG. 6.

FIG. 9 is a top view of a TRNG with a cell array matrix surfacecircumscribed by the radioactive source (with extension) surface, andcell/detectors of varying size.

FIG. 10 is a flow diagram of the various components that may be placedon the integrated circuit.

6.0 DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

Reference is made herein to some specific examples of the presentinvention, including any best modes contemplated by the inventor forcarrying out the invention. Examples of these specific embodiments areillustrated in the accompanying figures. While the invention isdescribed in conjunction with these specific embodiments, it will beunderstood that it is not intended to limit the invention to thedescribed or illustrated embodiments. On the contrary, it is intended tocover alternatives, modifications, and equivalents as may be includedwithin the spirit and scope of the invention as defined by the appendedclaims.

In the following description, numerous specific details are set forth inorder to provide a thorough understanding of the present invention.Particular example embodiments of the present invention may beimplemented without some or all of these specific details. In otherinstances, process operations well known to persons of skill in the arthave not been described in detail in order not to obscure unnecessarilythe present invention. Various techniques and mechanisms of the presentinvention will sometimes be described in singular form for clarity.However, it should be noted that some embodiments include multipleiterations of a technique or multiple mechanisms, unless notedotherwise. Similarly, various steps of the methods shown and describedherein are not necessarily performed in the order indicated, orperformed at all, in certain embodiments. Accordingly, someimplementations of the methods discussed herein may include more orfewer steps than those shown or described. Further, the techniques andmechanisms of the present invention will sometimes describe aconnection, relationship, or communication between two or more entities.It should be noted that a connection or relationship between entitiesdoes not necessarily mean a direct, unimpeded connection, as a varietyof other entities or processes may reside or occur between any twoentities. Consequently, an indicated connection does not necessarilymean a direct, unimpeded connection, unless otherwise noted.

The following list of example features corresponds to the attachedfigures and is provided for ease of reference, where like referencenumerals designate corresponding features throughout the specificationand figures:

-   Cell 5-   Silicon Substrate 8-   Detector 10-   Amplifier 15-   Memory 20-   Word Line 25-   Reset Line 30-   Bit Line 35-   Output Buffer/Memory 40-   TRNG Detector Chip with Cell Array Matrix 45-   Cell Array Matrix Surface 46-   Chip Cover/Enclosure 50-   Radioactive Source 55-   Radioactive Source Surface Projection (without extension) 56-   Radioactive Source Extension 57-   Radioactive Source Surface (with extension) 58-   Radioactive Source Surface Projection (with extension) 59-   Cavity 60-   Through Silicon Vias/Connections 65-   Processing Circuitry 70-   Control Block 75-   TRNG Processor 80

This is related to our previous published US patents and applicationslisted above, in which we described the general idea of using pure betaminus (electron emission) nuclear decay as a medium or source of entropyfor generating true random numbers by detecting emitted electronson-chip through an electronic sensor or array of sensors. In thisapplication, we would like to present the approach that allows for amuch faster or more efficient (larger number of bits per time unit)generation of random numbers on-chip from the very same source ofentropy i.e., ⁶³Ni.

Searching the BIPM Table of Radionuclides (2008), we find three abundantnuclides that produce pure beta-minus decay (only emission of anelectron and to conserve momentum some practically undetectableneutrino) in the range of energies below 512 keV (which is the energy ofelectrons that produces highly penetrable gamma rays, creating potentialradiation hazard) and having reasonable half-life times of more than tenyears. There are some other exotic nuclides listed in theabove-mentioned tables and fulfilling our requirements, but they aremostly intermediate products of decays of other exotic nuclides, hencenot practical for industrial applications. The three nuclides that areeasy to obtain and to process are:

-   -   a. 1. ³H tritium with the maximum energy of emitted electrons        being 18 keV (mean energy about 5.7 keV) and a half-life time of        about 12.4 years;    -   b. 2. ⁶³Ni nickel with the maximum energy of emitted electrons        being about 67 keV (mean energy about 17 keV) and a half-life        time of about 98.7 years;    -   c. 3. ¹⁴C carbon with the maximum energy of emitted electrons        being about 156 keV (mean energy about 45 keV) and a half-life        time of about 5,700 years.

When dealing with these low-energy radiative nuclei (except in the caseof gaseous tritium, which is very difficult to handle due to its highpermeation through solids and thus is better processed in the form ofgel or solid compound, as discussed in our U.S. Pat. No. 11,048,478),one has to note that because of the limited range of emitted electronsin solids (self-absorption of electrons), only a very thin layer ofradioactive material is externally active i.e., electrons emitted fromthe material are created only in a very thin layer. For example, ⁶³Nihas a maximum surface radioactivity of about 20 mCi/cm² independently ofincreasing the thickness of the material, cf. Belghachi et al.(2020)—only about 15 microns of such a material is relevant for externalradioactivity. We note that because 1 Ci equals about 3.7·10¹⁰decays/sec, the limit of 20 mCi/cm² corresponds to about 7.4·10⁸decays/(cm²·sec), or slightly less than 10⁹ decays/(cm²·sec). Thissuggests that a potential on-chip random number generator based on ⁶³Nican produce up to 1 billion bits per second from 1 cm² of the detectorarea, with more area taken by other electronics. The low energy oftritium beta decay makes the thickness of the active layer much thinnerthan for other pure beta decay radionuclides considered here, and thusgives a smaller maximum number of bits generated per area. On the otherhand, the half-life time of a given nuclide limits the total number ofelectrons emitted per time unit. For example, with 10 billion or 10¹⁰atoms of ⁶³Ni, only half will decay during 98.7 years, or about 2 persecond. For the ¹⁴C radionuclide with a very long half-life time, thisseverely limits the total possible radioactivity per time unit: oneneeds about a trillion or 10¹² atoms of ¹⁴C to get 2 decays per second,or 100× more carbon 14 nuclei are needed for the same radioactivity asfor nickel-63. In other words, about 12× larger area of radioactivematerial will be required to get the same effective number of decays persecond because the range of 45 keV electrons (average energy) in carbonis only about 8× larger than of 17 keV electrons (average energy) innickel, cf. Berger and Seltzer (1982) (the effective layer can be 8×thicker). Hence ⁶³Ni seems to be the sweet spot of efficiency persurface of radioactive material as a source of entropy for on-chiprandom number generators. However, its maximum radioactivity stilllimits the number of bits that can be generated on the chip because onecannot use detectors that are too large due to the so-called detectorreaction dead time. The shortest time between pulses that can bedetected depends on the low capacitance of the detector—this capacitanceincreases proportionally to the area of a detector. In our U.S. Pat. No.11,036,473, we suggested using an array of small detectors that can beapplied to overcome the abovementioned limitation. Here we describeproblems associated with such an approach and methods to solve theseproblems.

The main problem of all random number generators based on naturalphenomena like the emission of photons or electrons (known pure quantumprocesses) is the stability of the entropy source. In the case ofphoton-based devices, the source of photons is highly dependent ontemperature, supplied voltage, and long-term stability of light emitter(diode or laser), among other factors. For beta decays, resulting fromweak interactions inside the nuclei, there is no influence of externalfields (like gravitational or electromagnetic) on the timing ordirection of decays. Only at very low temperatures close to absolutezero and in very high magnetic fields do these decays show anisotropy orthe so-called parity violation, cf. Nobel Prize 1957. The only effect onthe stability of the radionuclide entropy source at normal conditions isits own half-life time that diminishes the number of decays in time. Asmentioned above, for ⁶³Ni the half-life time is about 98.7 years.According to an exponential equation that governs the number of decaysin time, N=N₀·e^(−λt) (N is the number of atoms left from the initialnumber N₀ after time t with λ=ln(2)/t_(1/2), where t_(1/2) is half-lifetime), after 2 years there will be still 98.6% of nickel-63 radioactiveatoms left; in other words, initially, nickel activity will onlydiminish by less than 0.7% per year. That can be easily corrected by theprocess of self-calibration mentioned in our U.S. Pat. No. 11,036,473(involving the changing of the read-out time).

Let us make simple estimates for the number of small detectors requiredto generate 1 billion (or 10⁹) bits per second with a ⁶³Ni entropysource. Assuming an individual detector radius of 11 microns and anentropy source with an activity of 15 mCi/cm², we get about 527 countsper second per detector area. 1,024 detectors read 1,000 times persecond will give us (as per our U.S. Pat. No. 11,036,473) the number of1 million bits per second. However, diode detectors (such as PIN, SPAD,or APD diode), unlike pixels of CCD cameras, cannot collect charge andhence require additional, simple memory circuits and readout lines toretain counts.

A simple cell 5 required to register any electron hits of the detectoris presented in FIG. 1. The cell 5 is comprised of silicon substrate 8with a detector 10, connected to an amplifier 15, and to the memory 20to store a detection event. The amplifier 15 amplifies the pulseproduced by the detector 10 when an electron hits the detector 10 andhas a write buffer at the output. This buffer writes “1” to the memory20 when an electron is detected. Subsequent detection events at the verysame detector will not change the state of the memory cell. Thus, thememory cell may contain only zero or one—the equivalent of one randombit. The cell 5 may have a word line 25 that, when signaled, causes thememory 20 to report its contents on the bit line 35. The reset line 30clears the cell of its memory to ready the cell for another detectionperiod. The individual cells can be arranged into an array as describedin the patent applications cited above. The state of all the cells 5 inthe array is read and stored in the output buffer/memory 40 via the bitlines 35 when this linear array is selected with “1” on the word line25. New contents in the output buffer/memory 40 replace the previousone.

FIG. 2A illustrates a TRNG detector chip comprising a cell array matrix45 and a chip cover/enclosure 50 and a radioactive source 55 (both madesemi-transparent so that the array of detectors/cells 5 can be seen).FIG. 2B is a cross-sectional view of a portion of the detector chip witha single detector cell from the array matrix of FIG. 2A. Thiscross-sectional view illustrates the chip cover/enclosure 50 and theradioactive source 55 (the preferred source is radioactive nickel),separated by a cavity 60 from the detector 10. The processing circuitry70 connects to detector 10 by through silicon vias connections (TSV) 65in the silicon substrate 8, thus protecting the processing circuit 70from the beta radiation i.e., the electrons emitted by the radioactivesource 55. The thickness of the TSV 65 may be selected to optimize theprotection of the processing circuitry 70. TSV are described e.g., inKnechtel J. et al. 2017. The Si wafer will have a total thickness ofmuch more than 10 microns so that all electrons emitted by theradioactive source 55 will be absorbed in it.

An issue not previously addressed in the cited patent applications isthat a true random number is optimally generated when the radiationsource generates the same flux of electrons on each detector. In otherwords, all the detectors in the array should be exposed to a uniformflux of electrons. If some areas are hotter than others, those areaswill report a detection more frequently, which will result in thegeneration of a number that is not random.

To arrive at a uniform flux, the source material should be infinite.Otherwise, detectors in the middle of an array will receive much largerdoses of electrons than those on the edge of an array. It is worthnoting that nuclear radiation sources described in the above-mentionedpatent like ⁶³Ni (beta decay) provide fluxes of electrons that areuniform in angular distribution (isotropic). This property allows for acalculation of the flux penetrating any given detector in the array,depending on its position. To do calculations, the following real-worlddimensions are used and illustrated in FIG. 3:

-   -   distance between source and chip surfaces a=2,000 μm    -   linear spread of the array b=10,000 μm    -   diameter of a single detector d=11 μm

The results are obtained using equations that define angles ofirradiation for a given detector placement, assuming that the flux isproportional to the irradiation angle:I˜Δθ  (1)

As illustrated in FIG. 4, three regions are contributing to the totalflux: on the left of the detector, just in front of the detector, and onthe right of the detector. The middle of the detector is positioned atx₀. For these three regions, the angles of irradiation from a pointsource located at x are described as functions of inverse tangents:

$\begin{matrix}{{{{\Delta{\theta(x)}} = {{\tan^{- 1}\left( \frac{a}{x_{0} - {{0.5}d} - x} \right)} - {\tan^{- 1}\left( \frac{a}{x_{0} + {{0.5}d} - x} \right)}}};}{x \in \left\lbrack {0,{x_{0} - {{0.5}d}}} \right\rbrack}} & (2) \\{{{{\Delta\theta}(x)} = {{\tan^{- 1}\left( \frac{x}{a} \right)} + {\tan^{- 1}\left( \frac{d - x}{a} \right)}}};{x \in \left\lbrack {{x_{0} - {{0.5}d}},{x_{0} + {{0.5}d}}} \right\rbrack}} & (3) \\{{{{\Delta{\theta(x)}} = {{\tan^{- 1}\left( \frac{a}{x - x_{0} - {{0.5}d}} \right)} - {\tan^{- 1}\left( \frac{a}{x - x_{0} + {{0.5}d}} \right)}}};}{x \in \left\lbrack {{x_{0} + {{0.5}d}},{{2c} + b}} \right\rbrack}} & (4)\end{matrix}$

In Eq. 4, c is the width of an extension region of a source material,discussed below and shown in FIGS. 6 and 7. Well-known formulas governinverse tangent functions and their integrals:

$\begin{matrix}{{\tan^{- 1}\left( {- x} \right)} = {- {\tan^{- 1}(x)}}} & (5) \\{{\int{{\tan^{- 1}\left( {1/x} \right)}{dx}}} = {{\frac{1}{2} \cdot {\log\left( {x^{2} + 1} \right)}} + {x \cdot {\tan^{- 1}\left( {1/x} \right)}}}} & (6) \\{{\lim_{x\rightarrow 0}\left\{ {x \cdot {\tan^{- 1}\left( \frac{1}{x} \right)}} \right\}} = 0} & (7)\end{matrix}$

Numerically solving the problem results in the graph shown in FIG. 5.This graph shows the large impact of a finite radiation source on fluxobserved on the edge detectors, as compared with those in the middle ofan array. Note this is when c is set to zero, as shown in FIG. 3.

Two ways of making the electron flux (or counts at each detector pertime unit) more uniform across the array are proposed here. The firstsolution is to extend the radiation source beyond the area of thedetectors, thus reducing the influence of the edge effect. Typically,the IC enclosure allows for a slightly larger radiation source than thearea of the IC. In our computational example, it is possible to add moreradiation source with a width of c=1,500 μm on each side of the squarearray. Distances for such a situation are presented in FIG. 6. FIG. 7illustrates the TRNG detector chip with a cell array matrix 45 ofcells/detectors (5, 10), that has a cell array matrix surface 46. By theaddition of the radioactive source extension 57, the radiation sourcesurface 58 is larger than and encompasses the cell array matrix surface46. This is also shown in FIG. 6, where the radioactive source surfaceprojection 59 extends beyond the edge of the cell array matrix surface46 (compare to radioactive source surface projection (without extension)56 and the cell array matrix surface 46 in FIG. 3). A projection is thetransformation of points and lines in one plane/surface onto anotherplane/surface by connecting corresponding points on the two planes withparallel lines. Here, the radioactive source surface projection 59 isthe projection of the radioactive source surface 58 onto the cell arraymatrix surface 46.

Plotting the detector radiation exposure as was done in FIG. 5, but nowwith c=1,500 μm, demonstrates that the radioactive source extension 57does indeed improve the uniformity, see FIG. 8, but still, the detectors10 in the middle of an array obtain much larger doses than those on theedge. The difference of electrons detected by the detectors in thisexample varies across the cell array matrix surface 46 by about 20% fromthe edges to the center point. Without the radioactive source extension57 (see FIG. 5) the difference across the cell array matrix surface 46is greater than 42%. Thus, the distance the radioactive source extension57 extends past the edge of the cell array matrix surface 46 can beselected to achieve an electron flux from the radioactive source thatvaries less than 40% over the cell array matrix surface 46, preferableless than 25%, more preferably less than 20% and most preferably lessthan 15%.

The second proposed solution, which may be used in conjunction with thefirst or in lieu of the first, is to increase the area of detectors thatare closer to the edge, thus increasing the number of electrons thatimpinge upon them per unit time. The calculation of the area increase isdone by using the ratio of fluxes that hit the center and edgedetectors. The calculations on how larger outer detectors need to beenlarged are presented in Table 1:

TABLE 1 position x₀ [μm] 1,505.5 2,500.0 3,500.0 4,500.0 5,500.0 6,500.07,500.0 8,500.0 9,500.0 10,500.0 11,494.5 detector size [μm] 13.7 12.311.6 11.2 11.1 11.0 11.1 11.2 11.6 12.3 13.7

In other words, most outer detectors in this particular case need to beenlarged (linearly) by about 2.7 μm or by about 25%. The final design,based on a two-dimensional array of detectors, will require additionalenlargement of the corner detectors by the square of the ratiocalculated above, i.e., by about 55% (area enlargement; corner detectorwill have a diameter of 17.1 μm, as compared with the diameter at thecenter equaling 11 μm as described above). All detectors in between thecenter and edges/corners will have their sizes increasedproportionately, as per calculations presented above. A method todetermine the various sizes of the detectors would include (a)determining the flux across the proposed array matrix surface; (b)calculating the difference between the maximum flux and the minimum fluxacross the proposed array matrix surface; (c) increasing the area of thedetectors of the array matrix as a function of the distance of thedetector from the point of maximum flux and the difference in step (c).

Generally, the radioactive source is centered above the array matrixsuch that the center point of the array matrix surface willcorrespondence to the maximum flux, with the flux diminishing as afunction of distance away from the center point. A TRNG detector chipwith cell array matrix 45 a of cells/detectors (5, 10) that vary in sizeaccording to this method is shown in FIG. 9. The cells/detectors (5, 10)are the largest in the corners, and the size of the cells increases thefarther away the detector is from the center point of the array matrix45 a. The TRNG detector chip 45 a shown in FIG. 9 also has theradioactive source extension 57 and a radiation source surface 58 largerthan and encompassing the cell array matrix surface 46.

FIG. 10 is a flow diagram of the various components that may be placedon the integrated circuit, using cell 5. The cells 5 each include asilicon substrate 8 with a detector 10 constructed to detect electronswithin the cavity 60 from the decay of the radioactive nickel andconstructed to produce a signal for the detected electrons. Theamplifier 15 connected to the detector 10 amplifies the signal andpasses it to the memory 20 for storage. A control block 75 is connectedto each cell 5 in the linear array. The contents of the memory 20 can bepassed to the output buffer/memory 40, from which a true random numbermay be generated by the TRNG processor 80.

Various example embodiments of the present apparatus, systems, andmethods demonstrate that ICs can be impregnated with radioactivematerial during manufacturing. Even with a very small amount ofradioactive nickel each, such chip can generate a significant number ofrandom bits per second; see Table 1 above: 6.4.10⁸ bits/(s·cm2). Thesebits can then be stored for later use in a solid-state memoryincorporated inside IC. Thus, such standalone TRNGs on-chip can easilyprovide on-demand thousands of multi-byte random numbers needed forencryption of communication channels (like voice or text messages) orfor processes requiring plenty of random numbers (like simulations orgaming).

Any of the suitable technologies, materials, and designs set forth andincorporated herein may be used to implement various example aspects ofthe invention, as would be apparent to one of skill in the art.

Although exemplary embodiments and applications of the invention havebeen described herein including as described above and shown in theincluded example Figures, there is no intention that the invention belimited to these exemplary embodiments and applications or to the mannerin which the exemplary embodiments and applications operate or aredescribed herein. Indeed, many variations and modifications to theexemplary embodiments are possible, as would be apparent to a person ofordinary skill in the art. The invention may include any device,structure, method, or functionality, as long as the resulting device,system, or method falls within the scope of one of the claims that areallowed by the patent office based on this or any related patentapplication.

The invention claimed is:
 1. A true random number generator (TRNG)comprising: a radioactive source defining a radioactive source surface;a cavity separating the radioactive source from an array of cellsdefining an array surface with an edge; wherein each cell in the arraycomprises a detector constructed to detect electrons within the cavityfrom the decay of the radioactive source and constructed to produce asignal for the detected energy; and wherein a projection of theradioactive source surface onto the array surface extends beyond theedge and encompasses the array surface; and a processor connected to thedetector and constructed to produce a true random number based on thesignal for the detected energy.
 2. The TRNG of claim 1, wherein theradioactive source is nickel.
 3. The TRNG of claim 1, wherein the arraysurface has a center point, and the size of the detector in each cell isbased on the distance of the detector from the center point.
 4. The TRNGof claim 1, further comprising a memory connected to each detector inthe array of cells, wherein the memory stores the produced signals fromthe detector.
 5. The TRNG of claim 4, wherein the processor produces thetrue random number based on the contents of the memory.
 6. The TRNG ofclaim 1, wherein the projection of the radioactive source surface ontothe array surface extends beyond the edge by a distance, and thedistance is selected to maintain an electron flux from the radioactivesource that varies less than 30% over the array surface.
 7. The TRNG ofclaim 1, wherein the projection of the radioactive source surface ontothe array surface extends beyond the edge by a distance, and thedistance is selected to maintain an electron flux from the radioactivesource that varies less than 25% over the array surface.
 8. The TRNG ofclaim 1, wherein the projection of the radioactive source surface ontothe array surface extends beyond the edge by a distance, and thedistance is selected to maintain an electron flux from the radioactivesource that varies less than 20% over the array surface.
 9. The TRNG ofclaim 1, further comprising an enclosure enclosing the radioactivesource, the cavity, and the array of cells.
 10. A true random numbergenerator (TRNG) comprising: a radioactive source; a cavity separatingthe radioactive source from an array of cells defining an array surfacewith a center point; wherein each cell in the array comprises a detectorconstructed to detect electrons within the cavity from the decay of theradioactive source and constructed to produce a signal for the detectedenergy; wherein the size of the detector in each cell is based on thedistance of the detector from the center point; and a processorconnected to the detector and constructed to produce a true randomnumber based on the signal for the detected energy.
 11. The TRNG ofclaim 10, wherein the radioactive source is nickel.
 12. The TRNG ofclaim 10, wherein the radioactive source defines a radioactive sourcesurface, and the array surface comprises an edge, wherein a projectionof the radioactive source surface onto the array surface extends beyondthe edge and encompasses the array surface.
 13. The TRNG of claim 10,further comprising a memory connected to each detector in the array ofcells, wherein the memory stores the produced signals from the detector.14. The TRNG of claim 13, wherein the processor produces the true randomnumber based on the contents of the memory.
 15. The TRNG of claim 10,further comprising an enclosure enclosing the radioactive source, thecavity, and the array of cells.
 16. A method for optimizing a truerandom number generator (TRNG), wherein the TRNG comprises an array ofcells, wherein each cell in the array comprises a detector that isconstructed to detect electrons from the decay of a radioactive sourceand to produce a signal for the detected energy, and the TRNG furthercomprises a processor connected to the detector and constructed toproduce a true random number based on the signal for the detectedenergy, the method comprising: (a) determining the electron flux fromthe radioactive source across a proposed array matrix surface; (b)calculating the difference between the maximum electron flux and theminimum electron flux across the proposed array matrix surface; (c)adjusting the area of the detectors of the array matrix as a function ofthe distance of the detector from the point of maximum electron flux andthe difference in step (b).